Introduction to the mathematical theory of compressible flow

Introduction to the mathematical theory of compressible flow / A. Novotný, I. Straéskraba.

This book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience. - ;Th...

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Bibliographic Details
Main Author: Novotný, A.
Other Authors: Straéskraba, I. (Ivan)
Format: eBook
Language:English
Published: Oxford ; New York : Oxford University Press, 2004.
Series:Oxford lecture series in mathematics and its applications ; 27.
Subjects:
Fluid dynamics > Mathematical models.
Compressibility.
compressibility.
compression.
TECHNOLOGY & ENGINEERING > Material Science.
Compressibility
Fluid dynamics > Mathematical models
Online Access:Click for online access
Table of Contents:
  • 1 Fundamental concepts and equations
  • 1.1 Some mathematical concepts and notation
  • 1.1.1 Basic notation
  • 1.1.2 Some useful inequalities in IR[sup(N)]
  • 1.1.3 Differential operators
  • 1.1.4 Gronwall's lemma
  • 1.1.5 Implicit functions
  • 1.1.6 Transformations of Cartesian coordinates
  • 1.1.7 Hölder-continuous and Lipschitz functions
  • 1.1.8 The symbols "o" and "O"
  • 1.1.9 Partitions of unity
  • 1.1.10 Measure
  • 1.1.11 Description of the boundary
  • 1.1.12 Measure on the boundary of a domain
  • 1.1.13 Classical Green's theorem
  • 1.1.14 Lebesgue spaces.
  • 1.1.15 Lebesgue's points
  • 1.1.16 Absolutely continuous functions
  • 1.1.17 Absolute continuity of integrals with respect to measurable subsets
  • 1.1.18 Some theorems from integration theory
  • 1.2 Governing equations and relations of gas dynamics
  • 1.2.1 Description of the flow
  • 1.2.2 The transport theorem
  • 1.2.3 The continuity equation
  • 1.2.4 The equations of motion
  • 1.2.5 The law of conservation of the moment of momentum. Symmetry of the stress tensor
  • 1.2.6 Inviscid and viscous fluids
  • 1.2.7 The energy equation
  • 1.2.8 The second law of thermodynamics and the entropy.
  • 1.2.9 Principle of material frame indifference
  • 1.2.10 Newtonian fluids
  • 1.2.11 Conservative and dissipation form of the energy equation for Newtonian fluids
  • 1.2.12 Entropy form of the energy equation for Newtonian fluids
  • 1.2.13 Some consequences of the Clausius-Duhem inequality
  • 1.2.14 Equations of state
  • 1.2.15 Adiabatic flow of a perfect inviscid gas
  • 1.2.16 Compressible Euler equations
  • 1.2.17 Compressible Navier-Stokes equations for a perfect viscous gas
  • 1.2.18 Barotropic flow of a viscous gas
  • 1.2.19 Speed of sound
  • 1.2.20 Simplified models.
  • 1.2.21 Initial and boundary conditions
  • 1.3 Some advanced mathematical concepts and results
  • 1.3.1 Spaces of Hölder-continuous and continuously diffrentiable functions
  • 1.3.2 Young's functions, Jensen's inequality
  • 1.3.3 Orlicz spaces
  • 1.3.4 Distributions
  • 1.3.5 Sobolev spaces
  • 1.3.6 Homogeneous Sobolev spaces
  • 1.3.7 Tempered distributions
  • 1.3.8 Radon measure and representation of C[sub(B)](])*
  • 1.3.9 Functions of bounded variation
  • 1.3.10 Functions with values in Banach spaces
  • 1.3.11 Sobolev imbeddings of abstract spaces
  • 1.3.12 Some compactness results.
  • 1.4 Survey of concepts and results from functional analysis
  • 1.4.1 Linear vector spaces
  • 1.4.2 Topological linear spaces
  • 1.4.3 Metric linear space
  • 1.4.4 Normed linear space
  • 1.4.5 Duals to Banach spaces and weak( -*) topologies
  • 1.4.6 Riesz representation theorem
  • 1.4.7 Operators
  • 1.4.8 Elements of spectral theory
  • 1.4.9 Lax-Milgram lemma
  • 1.4.10 Imbeddings
  • 1.4.11 Solution of nonlinear operator equations
  • 2 Theoretical results for the Euler equations
  • 2.1 Hyperbolic systems and the Euler equations
  • 2.1.1 Zero-viscosity Burgers equation.

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